The two-dimensional heat distribution under quasi-stationary state due to linear moving heat source of infinate plate can be expressed :
u=
qe-xv/2h2/2π
bcph2 K0(2√ γ) ; where γ=(4
a2h2+
v2)/16
h4(
x2+
y2)
And the isotherm for it may be approximately expressed as follows :
C-
a0Y=√
R2+
X2+log|√
R2+1-1|,
Y=√
R2-
X2,
where α
0=
vα
1/√4
a2h2+
v2, β
0=4
h2β
1/√4
a2+
h2+
v2;α
1=0.96, β
1=0.16,
and C=integral constant.
As far as the immediate neighbourhood of heat source is concerned, this isotherm may be substituted by ellipse which can be represented by the following equation:
(1-2α′
2C)
x2+
y2+2α
0′
Cx=0; α
0′=α′
v/2
h2, α=2.5
Further the graphical method for defining the isotherm is described (Fig. 8) with regard to the geometrical significance of this expression.
The main charrcteristics of the isotherm clarified through the graphical method are as follows: (i) The isotherm in this case takes form of an egg top-heavy in the direction of welding progress.
(ii) In the neighbourhood of heat source, all of these isotherms approach circles.
(iii) In the ZONE sufficiently detached from heat source, these curves tend to be the more flattened under the higher speed of welding.
On the other hand, study of the change of tangent will contribute to fundamental theory of "the formation of beardlike Lüders' lines clustered in series in the part of base metal adjacent to welding bead."
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